eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-03-05
7:1
7:22
10.4230/LIPIcs.ICDT.2018.7
article
A More General Theory of Static Approximations for Conjunctive Queries
Barceló, Pablo
Romero, Miguel
Zeume, Thomas
Conjunctive query (CQ) evaluation is NP-complete, but becomes tractable for fragments of bounded hypertreewidth. If a CQ is hard to evaluate, it is thus useful to evaluate an approximation of it in such fragments. While underapproximations (i.e., those that return correct answers only) are well-understood, the dual notion of overapproximations that return complete (but not necessarily sound) answers, and also a more general notion of approximation based on the symmetric difference of query results, are almost unexplored.
In fact, the decidability of the basic problems of evaluation, identification, and existence of those approximations, is open.
We develop a connection with existential pebble game tools that allows the systematic study of such problems. In particular, we show that the evaluation and identification of overapproximations can be solved in polynomial time. We also make progress in the problem of existence of overapproximations, showing it to be decidable in 2EXPTIME over the class of acyclic CQs. Furthermore, we look at when overapproximations do not exist, suggesting that this can be alleviated by using a more liberal notion of overapproximation. We also show how to extend our tools to study symmetric difference approximations. We observe that such approximations properly extend under- and over-approximations, settle the complexity of its associated identification problem, and provide several results on existence and evaluation.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol098-icdt2018/LIPIcs.ICDT.2018.7/LIPIcs.ICDT.2018.7.pdf
conjunctive queries
hypertreewidth
approximations
pebble games